PAPER   FOLDING  AND  CUTTING 

A   SERIES  OF 

FOLDINGS    AND   CUTTINGS 

ESPECIALLY   ADAPTED    TO 

KINDERGARTENS    AND    PUBLIC    SCHOOLS 

BY 

KATHERINE    M.    BALL 


BOSTON 
THE    PRANG    EDUCATIONAL    COMPANY 


COPYRIGHT,  1892,  BY 
THE   PRANG   EDUCATIONAL   COMPANY. 


stack 

Annex 

**•  • 


AUTHOR'S    PREFACE. 

T77VERY  scheme  for  art  education  must  necessarily  embrace 
*—  '     the  study  of  geometric  plane  figures  and  their  mechan- 
ical construction. 

The  prescribed  methods  for  this  construction  have  been 
difficult,  complicated,  consuming  much  time,  and,  if  learned  at 
all,  were  easily  forgotten. 

Children  would  easily  follow  a  dictation  which  would  result 
in  an  octagon,  hexagon,  pentagon,  etc.,  but  were  unable  to 
repeat  it  independently  the  following  day. 

After  various  unsuccessful  attempts  to  simplify  the  method 
of  drawing  these  figures,  my  attention  was  called  to  paper 
folding  and  cutting. 

The  ease  and  interest  with  which  the  children  would  make 
the  four-pointed  star,  the  four-leaved  rosette,  and  the  equi- 
lateral triangle,  as  outlined  by  The  Prang  Course  of  Drawing, 
suggested  that  possibly  other  figures,  such  as  the  crosses,  the 
trefoil,  the  quatrefoil,  the  octagon,  the  hexagon,  and  pentagon, 
might  be  made  in  a  similar  manner. 

3 


I 


2065936 


4  AUTHOR'S    PREFACE. 

After  much  thought  and  study,  I  discovered  the  principle 
underlying  such  construction  of  all  regular  plane  geometric 
figures.  It  is  simple,  and  within  the  comprehension  of  very 
young  children. 

It  is  a  great  help  in  teaching  simple  design,  inasmuch  as 
the  children  make  their  figures  from  paper  instead  of  drawing 
them,  thus  dealing  with  the  concrete  rather  than  the  abstract 
thing,  and  by  so  doing  they  get  broad,  simple  effects,  instead 
of  the  confusing  and  meaningless  arrangement  of  lines  called 
designs.  Inasmuch  as  it  consumes  very  little  time,  the  child 
can  make  a  second  or  third  trial  in  the  same  lesson,  correcting 
the  unsatisfactory  parts,  thus  enabling  them  to  make  three 
figures  where  before  they  made  one. 

Again,  these  exercises  will  be  found  to  be  valuable  in 
making  patterns  for  the  designs  in  colored  papers,  which  are 
now  taking  the  place  of  the  decorative  drawing  in  the  drawing- 
books. 

I  have  taken  great  pleasure  in  arranging  this  series  of 
exercises,  hoping  that  they  may  be  a  source  of  help  to  all 
teachers  interested  in  Art  Education  and  Manual  Training,  and 
that  they  may  give  a  new  impetus  to  form  study  and  design, 
by  being  associated  with  paper  folding  and  cutting,  which  is 
always  a  source  of  delight  to  the  children. 

KATHERINE    M.    BALL. 


CONTENTS. 


PAGE 

THE  PRINCIPLES  UNDERLYING  THE  WORK 7 

CHAPTER   I. 
GENERAL  SUGGESTIONS 9 

CHAPTER   II. 
METHOD  OF  PRESENTATION .11 

CHAPTER   III. 
EVOLUTION  OF  UNITS  AND  THEIR  APPLICATION  IN  DESIGN        .        .       17 

CHAPTER   IV. 
FOLDINGS  AND  CUTTINGS  FROM  THE  SQUARE  AND  CIRCLE: 

Circle,  Square.  Four-pointed  Star,  Quatrefoil,  Crosses,  and  Rosettes       22 

CHAPTER    V. 
FOLDINGS  AND  CUTTINGS  FROM  THE  SQUARE  AND  CIRCLE: 

Equilateral  Triangle,  Three-pointed  Star,  Trefoil,  and  Three-leaved 
Rosettes,  Hexagon,  Six-pointed  Star,  Hexafoil,  and  Six-Leaved 
Rosettes 27 

5 


6  CONTENTS. 

CHAPTER  VI. 

PAGE 

FOLDINGS  AND  CUTTINGS  FROM  THE  SQUARE  AND  CIRCLE: 

Pentagon,  Five-pointed  Star,  Cinquefoil,  and  Five-leaved  Rosettes      33 

CHAPTER  VII. 
FOLDINGS  AND  CUTTINGS  FROM  THE  SQUARE  AND  CIRCLE  : 

Heptagon  Seven-pointed  Star.  Heptafoil,  and  Seven-leaved  Rosettes      37 

CHAPTER   VIII. 
FOLDINGS  AND  CUTTINGS  FROM  THE  SQUARE  AND  CIRCLE: 

Nonagon,  Nine-pointed  Star,  Nonafoil,  and  Nine-leaved  Rosettes     .       40 

CHAPTER   IX. 
BORDERS 43 


PAPER   FOLDING   AND   CUTTING. 


A  simple  method  of  making  regular  plane  geometric  figures  from  a  square, 
a  circle,  or  any  regular  or  irregular  geometric  plane  figure,  by  means  of 
folding  in  such  a  manner  that  one  clip  of  the  scissors  will  give  the 
desired  result. 


PRINCIPLES   UNDERLYING  THE   WORK. 

THE  principle  upon  which  this  folding  is  made  is  the 
division  of  the  360°  of  the  circle,  or  imaginary  circle, 
contained  within  the  enclosing  plane  figure  into  as  many  parts 
as  there  are  sides  or  angles  to  the  figure. 

The  paper  may  be  square,  circular,  or  of  any  regular  or 
irregular  shape. 

We  fold  it  into  two  equal  parts,  as  in  the  circle  (or  as  near 
equal  as  can  be  obtained  in  the  other  figure);  this  gives  the 
1 80°  fold. 

By  bisecting  and  folding,  we  get  the  90°  fold. 

By  dividing  the  180°  fold  into  two  and  a  half  parts,  and 
folding,  we  get  the  72°  fold. 

7 


8  PAPER    FOLDING   AND   CUTTING. 

By  trisecting  the  180°  fold,  and  folding,  we  get  the  60°  fold. 

By  dividing  the  180°  fold  into  three  and  a  half  parts,  and 
folding,  we  get  the  51 2°  fold. 

By  bisecting  the  90°  fold,  and  folding,  we  get  the  45°  fold. 

By  dividing  the  180°  fold  into  four  and  a  half  parts,  and 
folding,  we  get  the  40°  fold. 

By  cutting  each  of  these  folds  so  that  the  result  will  be  an 
isosceles  triangle,  we  get  from  the  90°  fold  the  square ;  from 
the  72°  fold,  the  pentagon;  from  the  60°  fold,  the  hexagon; 
from  the  5 if-0  fold,  the  Jieptagon ;  from  the  45°  fold,  the  octagon ; 
and  from  the  40°  fold,  the  nonagon. 

For  the  equilateral  triangle  it  is  necessary  to  cut  the  60° 
fold  so  that  the  result  will  be  a  right-angled  triangle. 

The  accuracy  of  the  result  of  this  construction  will  naturally 
depend  upon  the  accuracy  of  the  folding  and  cutting. 


CHAPTER    I. 

GENERAL    SUGGESTIONS. 

THESE   folding   and    cutting   exercises   were   prepared   in 
order  to  give  the  children  a  short  cut  to  making  designs 
in  colored  papers. 

It  is  not  the  intention  to  fold  and  cut  the  colored  papers, 
but  to  make  a  pattern  from  white  paper  by  this  process,  the 
pattern  to  be  placed  on  the  back  of  the  colored  paper  and 
drawn  around.  By  cutting  on  this  drawn  line  we  get  the 
design. 

CUTTING. 

Teach  the  children  to  hold  the  scissors  easily  and  comfort- 
ably. In  cutting  long  lines,  the  scissors  should  be  opened  widely, 
so  that  the  entire  length  may  be  cut  at  one  time.  In  cutting 
curved  lines,  the  scissors  and  paper  should  approach  each  other 
equally,  both  describing  the  curve.  In  cutting  around  small 
curves  into  small  places,  it  will  be  found  necessary  to  use  the 
points  of  the  scissors  with  very  short  cuts. 

PASTING. 

Apply  to  the  terminal  points  of  the  design,  with  a  tooth- 
pick, small  pieces  of  paper,  or  brush,  the  smallest  possible 

9 


10  PAPER    FOLDING   AND   CUTTING. 

amount  of  paste.  Lay  a  blotter  or  piece  of  paper  on  the 
design,  and  rub  quite  hard  on  the  pasted  places  without  moving 
the  overlying  paper.  Place  the  result  under  some  weight  which 
will  be  sufficient  to  press  it  evenly  until  dry. 

ROSETTES. 

In  all  rosettes,  arrangements  having  repeats  radiating  from 
a  centre,  arrangements  which  are  not  figures  complete  in  them- 
selves, a  centre-piece  should  be  applied.  It  should  be  the  same 
color  as  the  units,  and  generally  occupy  about  a  third  of  the 
width  of  the  design. 


For  further  information  concerning  color,  making  arrange- 
ments, etc.,  refer  to  the  Prang  color  manual,  called  "  Color 
Instruction :  Suggestions  for  a  Course  of  Instruction  in  Color 
for  Public  Schools. 


CHAPTER   II. 

METHOD    OF  PRESENTATION. 

THIS    work  is  intended  to   follow  the   simple  outline  for 
folding  found  in  "The  Prang  Primary  Manual,"  therefore 
it  is  unnecessary  to  go  into  detail  as  to  preliminary  exercises. 

The  children,  having  learned  to  fold  edge  to  edge  and 
corner  to  corner,  having  bisected,  trisected,  and  quadrisected 
paper  by  folding,  are  now  ready  to  take  up  the  construction  of 
geometric  figures,,  stars,  rosettes,  and  borders. 

The  method  of  presentation  embraces  dictation,  imitation, 
and  imagination. 


3                             4 

Q 

3                               < 

( 

2 

/ 

40? 

) 

FIG. 


F.G.2 


F.&.3 


F.G-4 


With  the  square  in  the  hands  of  the  children,  they  bisect  it 
by  folding  1-2  on  3-4,  as  in  Fig.  i,  obtaining  Fig.  2.  Again 
they  bisect  Fig.  2  by  folding  1-2  on  3-4,  obtaining  Fig.  3. 


12 


PAPER    FOLDING   AND   CUTTING. 


Holding  Fig.  3  by  the  closed  corner  (which  is  the  centre 
of  the  original  square)  in  the  left  hand,  ask  the  children  what 
kind  of  a  figure  they  would  get  by  cut- 
ting a  curved  line,  concave  to  the  centre 
of  the  square  or  curving  outward,  con- 
necting points  i  and  2. 

After  they  have  worked  upon  their 
imagination  for  the  result,  let  them  make 
the  trial,  comparing  results. 
Next  ask  them  to  tell  you  what  kind  of  a  figure  they  would 
get  by  connecting  1-2  with  a  curved  line  curving  inward. 
They  may  not  be  able  to  describe  it  in  words,  but  may  make  a 
simple  drawing  on  their  slates  or  paper.  Have  them  make  the 
cut  and  again  compare  results.  They  may  then  in  like  manner 
connect  i  and  2  with  a  straight  line. 

They  may  now  fold  to  Fig.  4,  page  1 1.  By  folding  to  Fig.  3 
and  then  folding  i  on  2,  they 
will  get  Fig.  4.  Reversing  it 
and  holding  the  fold  at  the 
original  square's  centre,  o, 
what  will  they  get  by  cutting 
a  straight  line  from  i  to  2,  as 
a  ?  or  a  curved  line,  as  b  ? 
Both  exercises  may  be  cut. 

Now  ask  the  children  how  many  can  fold  and  cut  a  figure 
from  a  drawing  on  the  board.  Draw  the  quatrefoil  c,  page  13, 
on  the  board,  and  let  the  children  make  the  trial. 


METHOD   OF    PRESENTATION. 


13 


V 


Those  who  fail  may  be  assisted  in  this  manner :  Give  them 
a  fresh  square  and  ask  them  to  draw  the  quatrefoil  upon   it; 
then  fold  to  Fig.  4,  keeping  the  drawn  lines 
on  top. 

Ask  the  children  what  the  repeating  unit 
is.     (A  circle.)     Ask  how  much   of  the   re- 
peating unit  can  be  seen  on  the  fold.    (Half.) 
By  cutting  on  the  drawn  line,  they  will  get 
c  the  figure. 

If  the  fold  is  not  held  at  the  closed  corner,  o,  when  cutting, 
the  children  may  be  much  surprised  to  find  they  have  a  num- 
ber of  small,  meaningless 
pieces  of  paper  instead 
of  a  completed  figure. 
A  little  experience  will 
soon  correct  this. 

Figures  like  those  at 
the  right  may  be  put  on 
the  board,  which  the  chil- 
dren may  make. 

Frequently  the  chil- 
dren will  get  a  fair  imi- 
tation of  the  drawing, 
yet  their  proportion  of 
parts  may  be  such  as  to 

make  an  undesirable  result.     Then  it  will  be  necessary  to  lead 
them  to  analyze  the  drawing,  to  enable  them  to  more  closely 


14 


PAPER    FOLDING   AND   CUTTING. 


observe  it.  For  instance,  in  the  quatrefoil,  ask,  What  kind  of 
curves  are  to  be  found  ?  Where  does  the  curve  begin  and 
where  does  it  end  ?  At  what  point  on  the  diameter  do  the 
curves  meet,  and  what  kind  of  an  angle  do  they  make  ?  How 
near  the  corner  of  the  square  does  the  curve  come  ?  etc. 

After  a  series  of  such  questions,  have  the  children  make  a 
second  or  a  third  trial,  until  they  get  something  which  is  satis- 
factory. 

The  folding  and  cutting  do  not  consume  much  time ;  for  this 
reason  it  will  be  found  that  the  children  can  accomplish  more 
by  cutting  than  by  drawing  in  the  given  time. 

FIGURES    HAVING    THREE   OR    SIX    PARTS. 

In  taking  up  figures  having  three  or  six  parts,  we  must  show 
the  children  that,  in  order  to  get  three  or  six  parts,  the  whole 
square  must  first  be  divided  into  three  or  six  parts. 


T.G-.  I 


F.&.  2 


Thus  far  the  children  have  divided  the  paper  by  bisecting 
or  trisecting  the  sides  and  connecting  points  of  division,  as 
Fig.  i.  Now  we  want  a  division  which  is  made  by  lines  radi- 


METHOD   OF    PRESENTATION. 


15 


ating  from  the  centre,  as  Fig.  2.  In  Fig.  i,  we  divide  the  space 
into  parts  having  equal  size  and  shape ;  in  Fig.  2,  we  divide 
the  space  so  that  the  angles  at  the  centre  of  the  square  will 
be  equal. 

It  is  a  very  easy  matter  to  make  a  division  having  eight 
equal  angles,  as  all  it  requires  is  to  fold  diameters  and  diago- 
nals ;  but  one  having  three  or  six  is  much  more  difficult. 

As  six  embraces  three,  we  will  take  six  first.  Ask  the  chil- 
dren to  make  a  trial,  first  placing  a  point  in  the  centre  of  the 
square,  and  drawing  the  division  lines  radiating  from  it,  as  a. 

Have  them  test  the  accuracy  by  folding  I  on  2,  and  then 
into  thirds,  to  see  if  the  parts  are  equal. 


If  it  is  found  that  the  division  of  the  square  is  too  difficult, 
try  the  circle,  as  b,  in  a  similar  manner.  Inasmuch  as  the 
radiating  lines  will  be  of  the  same  length,  it  may  be  better 
understood. 

It  will  now  be  an  easy  matter  to  lead  them  to  the  folds 
as  given  for  all  three  and  six  leaved  rosettes. 


16 


PAPER    FOLDING    AND   CUTTING. 


FIGURES    HAVING    FIVE    PARTS. 


For  figures  having  five  parts,  the  square  must  be  divided 
into  five  parts,  the  dividing  lines  radiating  from  the  centre  and 
making  the  five  central  angles  the  same,  as  c. 

If  the  children  cannot  comprehend  this,  have  them  use  a 
circle,  as  d,  and  it  may  be  simpler.  Then  try  the  division  of 

the  square  afterwards. 

If  the  whole  square  is  divided  into 
five    parts,    the    half    square    must   be 
divided  into  two  parts  and  a  half,  as  c. 
It  will  now  be  an  easy  matter,  fold- 
«  ing  from  o,   to  fold    i   on   2,   and  the 

remaining  half    part  underneath,  thus  giving  us  the  fold  for 
five-leaved  rosettes. 


CHAPTER    III. 

THE   EVOLUTION    OF   UNITS   AND    THEIR   APPLICATION 
IN    DESIGN. 

THE  general  proportion  and  the  simple  and  shapely  outline 
of  the  kite  make  it  the  type  for  many  figures  used  as 
repeats  in  design ;   any  slight  modification   of  its  outline  will 
produce  a  new  figure,  as  shown  in  these  illustrations :  — 


'7 


IS 


PAPER    FOLDING    AND   CUTTING. 


In  the  kite,  and  the  units  based  on  it,1  we  find  the  greatest 
width  above  the  centre. 


1  This  "  Evolution  of  Units  "  is  taken  from  "  The  Prang  Course  in  Drawing." 


THE    EVOLUTION    OF   UNITS.  19 

There  are  other  pleasing  historic  repeats,  in  which  the 
greatest  width  is  below  the  centre.  Examples  of  the  kind 
are  given  in  these  illustrations  :  — 


The  upper  and  lower  rows  are  Moorish  ;  the  middle  row  is 
Gothic. 


20 


PAPER    FOLDING    AND    CUTTING 


a 


In  exercises  in  invention,  have  the  child  modify  the  kite, 
making  his  own  unit  and  applying  it  to  the  different  geometric 
figures.  While  the  same  unit  may  be  used  for  all  the  designs, 
its  adaptation  to  the  spaces  of  the  different  figures  must  neces- 
sarily change  its  proportions,  making  it  wider,  as  in  the  square, 
and  very  much  narrower,  as  in  the  octagon. 

Inferring  that  the  child  has  modified 
the  kite  intd  this  unit,  <?,  he  may  fold  the 
square,  from  which  the  design  is  to  be  cut, 
to  Fig.  4  of  Chapter  II.,  and  draw  on  it 
half  of  the  unit,  as  b.  If  he  should  cut 
from  o  through  I  to  3,  his  result  would  be 
four  separate  pieces,  as  there  would  be  noth- 
ing to  hold  it  together  at  the  centre ;  but, 
by  cutting  from  i  to  2,  point  2  being  the 
tangential  union  of  the  lines  2-1  and  0-3, 
the  design  will  be  complete,  as  c. 

He  will    now    be    interested    to   see   the 
effect  of   the  repetition   of   this  unit  in  the  c 

octagon,  the  triangle,  the  hexagon,  and  the  pentagon,  as  illus- 
trated in  Figs,  i,  2,  3,  4,  page  19. 

For  the  octagon,  he  must  fold  to  Fig.  5  of  Chapter  IV. ; 
for  the  triangle,  to  Fig.  4  of  Chapter  V.  ;  for  the  hexagon, 
to  Fig.  5  of  Chapter  V.  ;  and  for  the  pentagon,  to  Fig.  5  of 
Chapter  VI. ;  always  making  the  drawing  of  the  half  unit 
comfortably  fill  the  space  on  the  fold. 

Should   the   child   use  for  his   design  a   unit   that  in  itself 


THE    EVOLUTION    OF   UNITS. 


21 


0 


Fig.  2. 


Fig.  3.  Fig.  4. 

would  not  make  a  centre,  he  would  have  to  provide  for  this  in 
his  drawing  on  the  fold.  For  instance,  in  selection  a,  which  is 
the  kite,  should  he  cut  on  the  en- 
tire outline,  his  design  would  fall 
apart ;  but  by  drawing  a  centre 
on  it,  as  in  1-2  in  b,  and  cutting 

from  3  to  2  and  2  to    i,  as  in  c, 

...  ,,  ,  .  ,  a      0        °     °  c     0 

he  will  then  have  a  centre  which 

holds  the  units  together,  and  his  design  will  be  complete. 


CHAPTER    IV. 


FOLDINGS    AND    CUTTINGS    FROM    THE    SQUARE 
AND    CIRCLE. 

TO    make,    by   folding  and   cutting,    a    square,   a  circle,   a 
regular   octagon,    a    four-pointed    star,    an    eight-pointed 
star,  a  quatrefoil,  an  octafoil,  a  four-leaved  rosette,   an  eight- 
leaved  rosette,  from  a  square,  circle,  or  any  regular  or  irregular 

plane  figure. 

THE    SQUARE. 


0 

360° 


Tic,.  I 


For  Figs.  2,    3,   and  4,.  fold    i    on   2,  and  crease  with  the 

thumb-nail.      For    Fig,    5,    bisect 
the  angle  at  o  in  Fig.  4,  and  fold. 


THE    CIRCLE. 

Fold  to  Fig.  4,  and  cut  from 
i  to  2.  Points  i  and  2  are  equally 
distant  from  o. 


FOLDINGS   AND   CUTTINGS    FROM    THE   SQUARE. 


23 


THE    SQUARE. 

Fold  to  Fig.  4,  and  cut  from 
i  to  2.     Point  2  is  a  bisection  of 

3-0 


THE    REGULAR    OCTAGON. 

Fold  to  Fig.  4,  and  cut  from 
i  to  2.  Points  i  and  2  are  equally 
distant  from  O. 


THE    FOUR-POINTED    STAR. 

Fold  to  Fig.  4,  and  cut  from 
i  to  2.  Point  i  is  a  bisection  of 
3-0- 


THE    EIGHT-POINTED    STAR. 

Fold  to  Fig.  5,  and  cut  from 
i  to  2.  Point  2  is  nearer  to  3 
than  to  o. 


24 


PAPER    FOLDING    AND    CUTTING. 


THE    QUATREFOIL. 

Fold  to  Fig.  4,  and  draw  on 
the  fold  a  semicircle,  and  cut  from 
i  to  2.  Point  i  is  the  tangential 
union  of  the  semicircle  and  the 
line  3-4. 

THE    OCTAFOIL. 

Fold  to  Fig.  5,  and  draw  on 
the  fold  a  semicircle,  and  cut  from 
i  to  2.  Point  2  is  the  tangential 
union  of  the  semicircle  and  the 
line  3-0. 


FOUR-LEAVED    ROSETTES. 

Fold  to  Fig.  4,  and  cut  from  i  to  2. 


FOLDINGS   AND   CUTTINGS    FROM    TH£  CIRCLE. 


25 


THE    CIRCLE. 
Fold  I  on  2,  and  crease  with  the  thumb-nail. 


TIG  I 


FIG 


He,  3  FIG  4        FiG.5 


For  the  square,  fold  to  Fig.  3,  and  cut  from  i  to  2.  2 
For  the  octagon,  fold  to  Fig.  4,  and  cut  from  i  to  2. 
For  the  four-pointed  star,  fold  to  Fig.  4,  and  cut      3 
from  i  to  3.     Point  3  is  obtained  by  trisecting  2-0.  0 


26 


PAPER    FOLDING    AND    CUTTING. 


QUATREFOILS. 

Fold  to  Fig.  4,  and  cut  from  i  to  2. 


EIGHT-LEAVED    ROSETTES 
Fold  to  Fig.  5,  and  cut  from  i  to  2. 
2\\  I        ^  /\^\  2 

M, 


CHAPTER   V. 

FOLDINGS    AND    CUTTINGS    FROM    THE    SQUARE 
AND    CIRCLE.  —  Continued . 

TO   make,   by   folding  and  cutting,  an  equilateral  triangle, 
a    hexagon,    a   three-pointed    star,    a    six-pointed    star,    a 
trefoil,    a    hexafoil,    a    three-leaved    rosette,    and    a    six-leaved 
rosette,   from  a  square,   a  circle,   or  any  regular  or  irregular 

plane  figure. 

THE    SQUARE. 


T.G..   1 


Beginning  with  the  square,  Fig.  i,  fold  I  on  2,  folding  from 
o,  and  crease  with  the  thumb-nail,  thus  obtaining  Fig.  2. 

To  obtain  Fig.  3,  trisect  the  1 80°  fold  in  Fig.  2,  and  fold  the 
right  part  on  the  adjoining  one,  folding  from  o.  For  Fig.  4, 

27 


28 


PAPER    FOLDING    AND   CUTTING. 


fold  the  remaining  part,  seen  in  Fig.  3,  on  top  of  the  first  fold, 
and  crease.     For  Fig.  5,  bisect  and  fold  Fig.  4. 


THE    EQUILATERAL 
TRIANGLE. 

Fold  to  Fig.  4,  and  cut 
from  i  to  2.  The  line  1-2 
must  be  at  right  angles  to 
3-0- 


THE  REGULAR  HEXAGON. 

Fold  to  Fig.  4,  and  cut 
from  i  to  2.  Points  I  and 
2  must  be  equally  distant 
from  o. 


THE    THREE-POINTED    STAR. 

Fold  to  Fig.  4,  and  cut 
from  i  to  2.  Point  2  is  ob- 
tained by  quadrisecting  3-0. 


FOLDINGS   AND   CUTTINGS    FROM    THE   SQUARE. 


29 


THE    SIX-POINTED    STAR. 

Fold  to  Fig.  5,  and  cut 
from  i  to  2.  Point  2  is  ob- 
tained  by  trisecting  3-0. 


THE    TREFOIL. 

Fold  to  Fig.  4,  and  cut 
from  i  to  2.  Point  2  is  the 
intersection  of  the  line  3-0 
and  the  arc.  The  arc  should 
be  a  semicircle,  having  its 
centre  on  the  line  i-o. 


THE    TREFOIL. 

Fold  to  Fig.  4,  and  cut 
from  i  to  2.  The  arc  4-1 
should  be  a  quadrant,  with  3 
as  centre.  The  line  2-4-1 
must  be  at  right  angles  with 
5-0. 


30 


PAPER    FOLDING    AND   CUTTING 


THE    HEXAFOIL. 

Fold  to  Fig.  5,  and  cut 
from  i  to  2.  Point  2  is  the 
tangential  union  of  the  arc 
and  the  line  3-0.  The  arc 
should  be  a  semicircle,  hav- 
ing its  centre  on  the  line  i-o. 

THE    HEXAFOIL. 

Fold  to  Fig.  5,  and  cut 
from  i  to  2.  The  line  2-4 
must  be  at  right  angles  to 
i-o,  and  the  arc  3-1  should 
be  a  quadrant  with  4  as  cen- 
tre. 


THREE-LEAVED    ROSETTES. 
Fold  to  Fig.  3,  and  cut  from  i  to  2. 


FOLDINGS   AND   CUTTINGS    FROM    THE   CIRCLE. 


31 


THE    CIRCLE. 


FiG    I 


For  the  triangle,  fold  to  Fig.  3,  and  cut  from  i  to  2. 
For  the  hexagon,  fold  to  Fig.  4,  and  cut  from  i  to  2. 
For  the  six-pointed  star,  fold  to  Fig  5,  and  cut  from 
i  to  2.      Point  2  is  obtained  by  trisecting  3-0. 


32 


PAPER    FOLDING    AND   CUTTING. 


SIX-LEAVED    ROSETTES. 

Fold  to  Fig.  5,  and  cut  from  i  to  2. 


CHAPTER   VI. 

FOLDINGS    AND    CUTTINGS    FROM    THE    SQUARE 
AND    CIRCLE.  —  Continued. 


make,  by  folding  and  cutting,   a  regular  pentagon,  a 
^-     five-pointed  star,  a  cinquefoil,  and  a  five-leaved  rosette, 
from  a  square,  a  circle,  or  any  regular  or  irregular  plane  figure. 


THE    SQUARE. 


Fi&  I 


F.&  3 


Beginning  with  the  square,  Fig.  i,  fold   i   on  2,  and  crease 
with  the  thumb-nail,  thus  obtaining  Fig.  2, 

33 


34 


PAPER    FOLDING    AND   CUTTING. 


To  obtain  Fig.  3,  divide  the  180°  fold  into  two  and  a  half 
parts,  and  fold  the  right  part  on  to  the  adjoining  one,  folding 
from  o  in  Fig.  2.  For  Fig.  4,  reverse  the  position  of  the  fold, 
making  the  rear  face  the  front  face,  and  fold  the  remaining  half 
part,  seen  in  Fig.  3,  over  the  other  fold.  For  Fig.  5,  bisect 
Fig.  4,  folding  the  left  half  under  the  right  half. 


THE    REGULAR    PENTAGON. 

Fold  to  Fig.  4,  reverse  the 
position  of  the  fold,  and  cut 
from  i  to  2.  Points  i  and 
2  must  be  equally  distant 
from  o. 


THE    FIVE-POINTED    STAR. 

Fold  to  Fig.  5,  and  cut 
from  i  to  2.  Point  2  is 
nearer  to  o  than  to  3. 


FOLDINGS   AND   CUTTINGS   FROM    THE   SQUARE. 


35 


THE    CINQUEFOIL. 

Fold  to  Fig.  5,  and  cut  from 
i  to  2.  Point  2  is  the  tan- 
gential union  of  the  semicircle 
and  the  line  4-0.  The  arc 
3-2-1  is  a  semicircle  with  its 
centre  on  the  line  i-o. 


THE    CINQUEFOIL. 

Fold  to  Fig.  5,  and  cut  from 
i  to  2.  The  arc  4-1  should  be 
a  quadrant  with  3  as  centre, 
and  the  line  2-4-3  should  be 
at  right  angles  with  the  line 
i-o. 


THE    CINQUEFOIL. 

Fold  to  Fig.  5,  and  cut  from 
i  to  2.  The  arc  2-1  should  be 
a  quadrant  with  3  as  centre. 


36 


PAPER    FOLDING    AND   CUTTING. 


TIG.  I 


THE    CIRCLE. 


F.&.  2 


F.&.3 


Fio.5 


FIVE-LEAVED    ROSETTES. 

Fold  to  Fig.  5,  and  cut  from  i  to  2. 


CHAPTER   VII. 

FOLDINGS    AND    CUTTINGS    FROM    THE    SQUARE 
AND    CIRCLE.  — Continued. 

TO    make,   by  folding  and  cutting,    a  heptagon,    a  seven- 
pointed  star,  a  heptafoil,  and  a  seven-leaved  rosette,  from 
a  square,  circle,  or  any  regular  or  irregular  plane  figure. 


THE    SQUARE. 


0          0\ 
Tic  5  TIG  6 


Beginning  with  the  square,  Fig.  i,  fold   i   on  2,  and  crease 
with  the  thumb-nail,  thus  obtaining  Fig.  2. 

37 


38 


PAPER    FOLDING   AND   CUTTING. 


To  obtain  Fig.  3,  divide  the  180°  fold  into  two  and  a  third 
parts,  and  fold  the  right  part  on  the  adjoining  one,  folding  from 
o  in  Fig.  2.  For  Fig.  4,  reverse  the  position  of  the  fold, 
placing  the  rear  face  in  front,  and  fold  the  remaining  third  part 
over  the  other  fold.  For  Fig.  5,  fold  the  edge  i  to  adjoin  the 
edge  2  in  Fig.  4,  making  i-o  and  2-0  meet.  For  Fig.  6,  bisect 
the  fold  of  Fig.  5,  folding  the  left  half  under  the  right  half. 


THE    HEPTAGON. 

Fold  to  Fig.  5,  and  cut  from 
i  to  2.  Points  i  and  2  are 
equally  distant  from  o. 


THE    SEVEN-POINTED    STAR.  . 

Fold  to  Fig.  6,  and  cut  from 
i  to  2.  Point  2  is  nearer  to  4 
than  to  3. 


FOLDINGS  AND  CUTTINGS  FROM  THE  SQUARE. 


39 


THE    HEPTAFOIL. 

Fold  to  Fig.  6,  and  cut  from 
i  to  2.  Point  2  is  the  tangen- 
tial union  of  the  semicircle  and 
the  line  3-0.  The  semicircle 
must  have  its  centre  on  the 
line  i-o. 


THE  SEVEN-LEAVED  ROSETTE. 

Fold  to  Fig.  5,  and  cut  from 

i  to  2. 


CHAPTER   VIII. 

FOLDINGS    AND    CUTTINGS    FROM    THE    SQUARE 
AND    CIRCLE.  —  Concluded. 

TO    make,    by    cutting  and  folding,    a  regular  nonagon,  a 
nine-pointed  star,  a  nonafoil,  and  a  nine-leaved  rosette, 
from  a  square,  circle,  or  any  regular  or  irregular  plane  figure. 


THE    SQUARE. 


F.G  I 


0  ¥0 

FIG  5        TIG  6 


Beginning  with  the  square,  fold  i  on  2,  and  crease  with  the 
thumb-nail. 

40 


FOLDINGS   AND   CUTTINGS    FROM    THE    SQUARE. 


41 


To  obtain  Fig.  3,  divide  the  180°  fold  into  two  and  a  fourth 
parts,  and  fold  the  right  part  on  the  adjoining  one,  folding 
from  o  in  Fig.  2.  For  Fig.  4,  reverse  the  position  of  the  fold, 
making  the  back  face,  the  front  face,  and  fold  the  remaining 
fourth  part  over  the  other  fold.  For  Fig.  5,  bisect  Fig.  4  by 
folding  i  on  2,  placing  the  left  half  under  the  right  half.  For 
Fig  6,  bisect  Fig.  5  by  again  folding  I  on  2,  and  placing  the 
left  half  under  the  right  half. 


THE    REGULAR    NONAGON. 

Fold  to  Fig.  5,  and  cut  from 
i  to  2.  Points  i  and  2  are  equally 
distant  from  o. 


THE    NINE-POINTED    STAR. 

Fold  to  Fig.  6,  and  cut  from 
i  to  2.  Point  2  is  nearer  to  o 
than  to  3. 


42 


PAPER    FOLDING   AND   CUTTING. 


THE    NONAFOIL. 

Fold  to  Fig.  6,  and  cut  from 
I  to  2.  The  arc  1-2  is  a  quad- 
rant with  3  as  centre. 


THE    NINE-LEAVED    ROSETTE. 

Fold  to  Fig.  6,  and  cut  from 
i  to  2. 


CHAPTER    IX. 

BORDERS. 

A    BORDER    WHICH    HAS    AN     UPWARD    GROWTH. 

CUT  an  oblong  the  size  required  for  your  border.     Upon  it 
draw  marginal  bands  and  a  repeating  unit,  as  in  Fig.  i. 
To  obtain  Fig.  2,  fold  the  paper  into  as  many  parts   as   the 


Fio.  I 


Fi&.4  FIG.  5 

oblong  1-2-3-4  will  be  contained  in  it.  For  Fig.  3,  bisect 
Fig.  2  by  folding.  For  Fig.  4,  cut  from  i  to  2  for  the  upper 
marginal  strip,  and  from  3  to  4  for  the  unit  and  connecting 

43 


PAPER    FOLDING   AND   CUTTING. 


lower  marginal  strip.     For  Fig.  5,  mount  the  border  and  mar- 
ginal strip,  giving  them  the  same  relation  as  in  Fig.  I. 


OTHER    BORDERS. 


FiG.    I 


fie  2 


FiG.  3 


BORDERS. 


45 


FIG.  I 


Tic. 


FIG.  3 


University  of  California 

SOUTHERN  REGIONAL  LIBRARY  FACILITY 

405  Hi Igard  Avenue,  Los  Angeles,  CA  90024-1388 

Return  this  material  to  the  library 

from  which  it  was  borrowed. 


^22*91 


v/ft 

FEB  0'7lb95 


OK  2  MS  nflM 

;EC'C  --  U 


1  ATE  RECEIVED 


ABLE 


tS  BL19 

-r!!brary  Loans 

;  1 630  University  R  search  Library 
-x  951 575 

Angoles,  CA   SP095-1  575 


A     000  037  437     1 


